Method of generating and/or detecting synchronization sequences, synchronization method, transmitter unit and receiver unit

ABSTRACT

Method for forming and/or determining a synchronization sequence, a synchronization method, a transmitting unit and a receiving unit, the formation of synchronization sequences, which are based on partial signal sequences, includes a second partial signal sequence being repeated and modulated in the process by a first partial signal sequence.

BACKGROUND OF THE INVENTION

In signal transmission systems, such as mobile radio systems, it isnecessary for one of the communication partners (first transmissionunit) to detect specific fixed signals which are emitted by anothercommunication partner (second transmission unit). These can be, forexample, what are termed synchronization bursts for synchronizing twosynchronization partners such as radio stations, for example, or whatare termed access bursts.

In order to detect or identify such received signals reliably bycontrast with the ambient noise, it is known to correlate the receivedsignal continuously with a prescribed synchronization sequence over afixed time duration, and to form the correlation sum over the timeduration of the prescribed synchronization sequence. The range of thereceived signal, which yields a maximum correlation sum, corresponds tothe signal being searched for. Connected upstream, as what is termed atraining sequence, of the synchronization signal from the base stationof a digital mobile radio system is, for example, a synchronizationsequence which is detected or determined in the mobile station in theway just described by correlation with the stored synchronizationsequence.

Such correlation calculations are also necessary in the base station;for example in the case of random-access-channel (RACH) detection.Moreover, a correlation calculation is also carried out to determine thechannel pulse response and the signal propagation times of receivedsignal bursts.

The correlation sum is calculated as follows in this case:${Sm} = {\sum\limits_{i = 0}^{n - 1}{{E\left( {i + m} \right)}*{K(i)}}}$E(i) being a received signal sequence derived from the received signal,and K(i) being the prescribed synchronization sequence, i running from 0to n−1. The correlation sum Sm is calculated sequentially for a numberof temporally offset signal sequences E(i) obtained from the receivedsignal, and then the maximum value of Sm is determined. If k sequentialcorrelation sums are to be calculated, the outlay on calculation is k*noperations, a multiplication and addition being counted together as oneoperation.

The calculation of the correlation sums is, therefore, very complicatedand, particularly in real time applications such as voice communicationor video-telephony or in CDMA systems, requires powerful and expensiveprocessors which have a high power consumption during calculation. Forexample, a known synchronization sequence of length 256 chips (atransmitted bit is also termed a chip in CDMA) is to be determined forthe purpose of synchronizing the UMTS mobile radio system, which isbeing standardized. The sequence is repeated every 2560 chips. Since themobile station initially operates asynchronously relative to the chipclock, the received signal must be oversampled in order still to retainan adequate signal even given an unfavorable sampling situation. Becauseof the sampling of the I and Q components, this leads to256*2560*2*2=2621440 operations.

WO 96 39749 A discloses transmitting a synchronization sequence, a chipof the sequence itself being a sequence.

“Srdjan Budisin: Golay Complementary Sequences are Superior to PNSequences, Proceedings of the International Conference on SystemsEngineering, US, New York, IEEE, Vol. 1992, pages 101–104, XP 000319401ISBN: 0-7803-0734-8” discloses using Golay sequences as an alternativeto PN sequences.

It is an object of the present invention to specify methods forsynchronizing a base station with a mobile station, as well as tospecify both a base station and a mobile station, which permitssynchronization of a base station with a mobile station and which isreliable and favorable in terms of outlay.

SUMMARY OF THE INVENTION

In this case, firstly, the present invention is based on the idea offorming what is termed a “hierarchical sequence”; in particular, ahierarchical synchronization sequence y(i) which is based in accordancewith the following relationship on a first constituent sequence x1 oflength n1 and a second constituent sequence x2 of length n2:y(i)=x ₂(i mod n ₂)*x ₁(i div n ₂) for i=0 . . . (n ₁ *n ₂)−1

This design principle of a hierarchical synchronization sequenceenvisages a repetition of a constituent sequences in their full length,the repetitions being modulated with the value of the correspondingelement of the second constituent sequence. It is, thereby, possible toform synchronization sequences which can be determined easily when theyare contained in a received signal sequence. Such synchronizationsequences have good correlation properties and permit efficientcalculation of the correlation in a mobile station. It was possible toshow this via complex simulation tools created specifically for thispurpose.

Furthermore, the present invention is based on the finding that, in thecase of the use of a hierarchical sequence as synchronization sequencewhich is based on two constituent sequences, it is possible to achieve afurther reduction in complexity at the receiving end when at least oneconstituent sequence itself is a hierarchical sequence.

It is provided in this case that only one repetition of the first half(or another part) of the first constituent sequence is carried out,followed thereupon by the second half and its repetitions. Therepetitions are modulated once again with the value of the correspondingelement of the second constituent sequence. A parameter s is introducedwhich specifies the part of the constituent sequence which is repeatedas a coherent piece. The formula describing this generalized developedformulation for forming “generalized hierarchical sequences” runs:x ₁(i)=x ₄(i mod s+s·(i div sn ₃))·x ₃((i div s)mod n ₃), for i=0. . . .n ₃ ·n ₄−1For s=n₄, this relationship for describing “generalized hierarchicalsequences” is equivalent to the relationship explained above for forming“hierarchical synchronization sequences”.

Within the scope of the present invention, “constituent sequences” aswell as “partial signal sequences” are denoted as K1 and K2,respectively, or as x1 and x₁, respectively, or as x2 and x₂,respectively. “Synchronization sequences” or “synchronization codes” arealso denoted as “y(i)” or “K(i)”. Of course, “determination of asynchronization sequence” is also understood as the determination of thetemporal position of a synchronization sequence. The term “receivedsignal sequence” is also understood as a signal sequence which isderived from a received signal by demodulation, filtering, derotation,scaling or analog-to-digital conversion, for example.

A development of the present invention is based on the finding that, inthe case of the use of a hierarchical sequence as synchronizationsequence which is based on two constituent sequences, at least oneconstituent sequence being a Golay sequence, it is possible to achieve afurther reduction in complexity at the receiving end.

It was possible through the use of complicated simulations to findparameters for describing Golay sequences which are particularly wellsuited as constituent sequences.

Specific refinements of the present invention provide for usingconstituent sequences of length 16 to form a hierarchical 256 chipsequence; in particular, a synchronization sequence, a first constituentsequence being a Golay sequence, and a second constituent sequence beinga generalized hierarchical sequence whose constituent sequences arebased on two Golay sequences (of length 4). For example, x₂ is definedas the Golay sequence of length 16 which is obtained by the delay matrixD²=[8, 4, 1, 2] and the weight matrix W²=[1, −1, 1, 1]. x₁ is ageneralized hierarchical sequence, in which case s=2 and the two Golaysequences x₃ and x₄ are used as constituent sequences. x₃ and x₄ areidentical and are defined as Golay sequences of length 4 which aredescribed by the delay matrix D³=D⁴ =[1, 2] and the weight matrix W³=W⁴=[1, 1].

A Golay sequence a_(N), also denoted as a Golay complementary sequence,can be formed in this case using the following relationship:a ₀(k)=δ(k) and b ₀(k)=δ(k)a _(n)(k)=a _(n-1)(k)+W _(n) ·b _(n-1)(k−D _(n)),b _(n)(k)=a _(n-1)(k)−W _(n) ·b _(n-1)(k−D _(n)),k=0, 1, 2, . . . 2^(N),n=1, 2, . . . , N.

-   -   δ(k) Kronecker delta function    -   D Delay matrix    -   W Weight matrix

Additional features and advantages of the present invention aredescribed in, and will be apparent from, the following DetailedDescription of the Invention and the Figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a schematic of a mobile radio network.

FIG. 2 shows a block diagram of a radio station.

FIG. 3 shows a conventional method for calculating correlation sums.

FIGS. 4, 5, 6, 7 and 8 show block diagrams of efficient Golaycorrelators in connection with the teachings of the present invention.

FIG. 9 shows a diagram with simulation results.

DETAILED DESCRIPTION OF THE INVENTION

Illustrated in FIG. 1 is a cellular mobile radio network such as, forexample, the GSM (Global System for Mobile Communication), whichincludes comprises a multiplicity of mobile switching centers MSC whichare networked with one another and/or provide access to a fixed networkPSTN/ISDN. Furthermore, these mobile switching centers MSC are connectedto, in each case, at least one base station controller BSC, which canalso be formed by a data processing system. A similar architecture isalso to be found in a UMTS (Universal Mobile Telecommunication System).

Each base station controller BSC is connected, in turn, to at least onebase station BS. Such a base station BS is a radio station which can usean air interface to set up a radio link to other radio stations, whatare termed mobile stations MS. Information inside radio channels f whichare situated inside frequency bands b can be transmitted via radiosignals between the mobile stations MS and the base station BS assignedto these mobile stations MS. The range of the radio signals of a basestation substantially defines a radio cell FZ.

Base stations BS and a base station controller BSC can be combined toform a base station system BSS. The base station system BSS is alsoresponsible in this case for radio channel management and/or assignment,data rate matching, monitoring the radio transmission link, hand-overprocedures and, in the case of a CDMA system, assigning the spread codeset to be used, and transfers the signaling information required forthis purpose to the mobile stations MS.

For FDD (Frequency-Division Duplex) systems such as the GSM, it ispossible in the case of a duplex system to provide for the uplink u(mobile station (transmitting unit) to the base station (receivingunit)) frequency bands differing from those for the downlink d (basestation (transmitting unit) to the mobile station (receiving unit)). Anumber of frequency channels f can be implemented within the differentfrequency bands b via an FDMA (Frequency-Division Multiple Access)method.

Within the scope of the present application, the transmission unit isalso understood as a communication unit, transmitting unit, receivingunit, communication terminal, radio station, mobile station or basestation. Terms and examples used within the scope of this applicationfrequently refer also to a GSM mobile radio system; however, they arenot in any way limited thereto, but easily can be mapped by a personskilled in the art with the aid of the description onto other, possiblyfuture, mobile radio systems. Such systems would include, for example,CDMA systems; in particular, wide-band CDMA systems.

Data can be efficiently transmitted, separated and assigned to one ormore specific links and/or to the appropriate subscriber via an airinterface via multiple access methods. It is possible to make use forthis purpose of time-division multiple access TDMA, frequency-divisionmultiple access FDMA, code-division multiple access CDMA or acombination of a number of these multiple access methods.

In FDMA, the frequency band b is broken down into a number of frequencychannels f. These frequency channels are split up into time slots ts viatime-division multiple access TDMA. The signals transmitted within atime slot ts and a frequency channel f can be separated via spreadcodes, what are termed CDMA codes cc, that are modulated in alink-specific fashion onto the data.

The physical channels thus produced are assigned to logic channelsaccording to a fixed scheme. The logic channels are basicallydistinguished into two types: signaling channels (or control channels)for transmitting signaling information (or control information), andtraffic channels (TCH) for transmitting useful data.

The signaling channels are further subdivided into:

-   -   broadcast channels    -   common control channels    -   dedicated/access control channels DCCH/ACCH

The group of broadcast channels includes the broadcast control channelBCCH, through which the MS receives radio information from the basestation system BSS, the frequency correction channel FCCH and thesynchronization channel SCH. The common control channels include therandom access channel RACH. The bursts or signal sequences that aretransmitted to implement these logic channels can include, in this case,for different purposes synchronization sequences K(i), what are termedcorrelation sequences, or synchronization sequences K(i) can betransmitted on these logic channels for different purposes.

A method for synchronizing a mobile station MS with a base station BS isexplained now by way of example. During a first step of the initialsearch for a base station or search for a cell (initial cell searchprocedure), the mobile station uses the primary synchronization channel(SCH (PSC)) in order to achieve a time slot synchronization with thestrongest base station. This can be ensured via a matched filter or anappropriate circuit which is matched to the primary synchronization codecp (synchronization sequence) that is emitted by all the base stations.In this case, all the base stations BS emit the same primarysynchronization code cp of length 256.

The mobile station uses correlation to determine from a receivedsequence the received synchronization sequences K(i). In this case,peaks are output at the output of a matched filter for each receivedsynchronization sequence of each base station located within thereception area of the mobile station. The detection of the position ofthe strongest peak permits the determination of the timing of thestrongest base station modulo of the slot length. In order to ensure agreater reliability, the output of the matched filter can be accumulatedover the number of time slots in a non-coherent fashion. The mobilestation therefore carries out a correlation over a synchronizationsequence of length 256 chips as a matched-filter operation.

The synchronization code cp can be formed in this case according to ahierarchical synchronization sequence K(i) or y(i) using the followingrelationships from two constituent sequences x₁ and x₂ of length n₁ andn₂ respectively:y(i)=x ₂(i mod n ₂)*x ₁(i div n ₂) for i=0 . . . (n ₁ *n ₂)−1

The constituent sequences x₁ and x₂ are of length 16 (that is to say,n1=n₂=16), and are defined by the following relationships:x ₁(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1

x₁ is, thus, a generalized hierarchical sequence using the aboveformula, in which case s=2 is selected and the two Golay sequences x₃and x₄ are used as constituent sequences.

x₂ is defined as the Golay sequence of length 16 (N₂=2) which isobtained via the delay matrix D²=[8, 4, 1, 2] and the weight matrixW²=[1, −1, 1, 1].

x₃ and x₄ are identical Golay sequences of length 4 (N=2), which aredefined by the delay matrix D³=D⁴=[1, 2] and the weight matrix W³=W⁴=[1,1].

The Golay sequences are defined using the following recursiverelationship:a ₀(k)=δ(k) and b₀(k)=δ(k)a _(n)(k)=a _(n-1)(k)+W _(n) ·b _(n-1)(k−D _(n)),b _(n)(k)=a _(n-1)(k)−W _(n) ·b _(n-1)(k−D _(n)),k=0, 1, 2, . . . , 2^(N).n=1, 2, . . . , N.

-   -   a_(N) then defines the required Golay sequence.

FIG. 2 shows a radio station which can be a mobile station MS, whichincludes an operating unit or interface unit MMI, a control device STE,a processing device VE, a power supply device SVE, a receiving device EEand, if appropriate, a transmitting device SE.

The control device STE essentially includes a program-controlledmicrocontroller MC which can access memory chips SPE by writing andreading. The microcontroller MC controls and monitors all essentialelements and functions of the radio station.

The processing device VE also can be formed by a digital signalprocessor DSP, which can likewise access memory chips SPE. Addition andmultiplication also can be achieved via the processing device VE.

The microcontroller MC and/or the digital signal processor DSP and/orstorage devices SPE and/or further computing elements known as such to aperson skilled in the art can be combined in this case to form aprocessor device which is set up in such a way that the method of thepresent invention can be carried out.

The program data required for controlling the radio station and thecommunication cycle, as well as, in particular, the signalingprocedures, and information produced during the processing of signalsare stored in the volatile or nonvolatile memory chips SPE. Moreover,synchronization sequences K(i) which are used for correlation purposes,and intermediate results of correlation sum calculations can be storedtherein. The synchronization sequences K(i) within the scope of thepresent invention can, thus, be stored in the mobile station and/or thebase station. It is also possible for one or more of parameters fordefining synchronization sequences or partial signal sequences orpartial signal sequence pairs (K1(j); K2(k)) derived therefrom to bestored in the mobile station and/or the base station. It is alsopossible for a synchronization sequence K(i) to be formed from a partialsignal sequence pair (K1(j); K2(k)) and/or one or more parameters fordefining synchronization sequences or partial signal sequences derivedtherefrom in the mobile station and/or the base station.

In particular, it is possible to store in a base station, or in all thebase stations in a system, a synchronization sequence K(i) which isemitted at fixed or variable intervals for synchronization purposes.Constituent sequences (partial signal sequences) or parameters fromwhich the synchronization sequence K(i) stored in the base station canbe, or are, formed are stored in the mobile station MS and are used tosynchronize the mobile station with a base station in order to calculatethe correlation sum favorably in terms of computational outlay.

The storage of the synchronization sequences or the partial signalsequences or parameters also can be performed by storing appropriateinformation in arbitrarily coded form, and can be implemented with theaid of storage devices such as, for example, volatile and/or nonvolatilememory chips or via appropriately designed adder or multiplier inputs orappropriate hardware configurations which have the same effect.

The high-frequency section HF includes if appropriate, the transmittingdevice SE, with a modulator and an amplifier V, and a receiving deviceEE with a demodulator and, likewise, an amplifier. The analog audiosignals and the analog signals originating from the receiving device EEare converted via analog-to-digital conversion into digital signals andprocessed by the digital signal processor DSP. After processing, thedigital signals are converted, if appropriate, by digital-to-analogconversion into analog audio signals or other output signals and analogsignals that are to be fed to the transmitting device SE. Modulation ordemodulation, respectively, is carried out for this purpose, ifappropriate.

The transmitting device SE and the receiving device EE are fed with thefrequency of a voltage-controlled oscillator VCO via the synthesizerSYN. The system clock for timing processor devices of the radio stationalso can be generated via the voltage-controlled oscillator VCO.

An antenna device ANT is provided for receiving and for transmittingsignals via the air interface of a mobile radio system. The signals arereceived and transmitted in what are termed bursts that are pulsed overtime in the case of some known mobile radio systems such as the GSM(Global System for Mobile Communication).

The radio station also may be a base station BS. In this case, theloudspeaker element and the microphone element of the operating unit MMIare replaced by a link to a mobile radio network, for example via a basestation controller BSC or a switching device MSC. The base station BShas an appropriate multiplicity of transmitting and receiving devices,respectively, in order to exchange data simultaneously with a number ofmobile stations MS.

A received signal sequence E(1), which also can be a signal sequencederived from a received signal, of length W is illustrated in FIG. 3. Inorder to calculate a first correlation sum S0 in accordance with theformula specified at the beginning, elements of a first section of thisreceived signal sequence E(1) are multiplied in pairs by thecorresponding elements of the synchronization sequence K(i) of length n,and the length of the resulting partial results is added to thecorrelation sum S0.

In order to calculate a further correlation sum S1, as illustrated inthe FIG. 3, the synchronization sequence K(i) is shifted to the right byone element, and the elements of the synchronization sequence K(i) aremultiplied in pairs by the corresponding elements of the signal sequenceE(1), and the correlation sum S1 is formed again by summing the partialresults produced.

The pairwise multiplication of the elements of the synchronizationsequence by corresponding elements of the received signal sequence, andthe subsequent summation also can be described in vector notation as theformation of a scalar product, if the elements of the synchronizationsequence and the elements of the received synchronization sequence arerespectively combined to form a vector: ${S0} = {{\begin{pmatrix}{K(0)} \\\vdots \\{K(i)} \\\vdots \\{K\left( {n - 1} \right)}\end{pmatrix}*\begin{pmatrix}{E(0)} \\\vdots \\{E(i)} \\\vdots \\{E\left( {n - 1} \right)}\end{pmatrix}} = {{{K(0)}*{E(0)}} + \ldots + {{K(i)}*{E(i)}} + \ldots + {{K\left( {n - 1} \right)}*{E\left( {n - 1} \right)}}}}$${S1} = {{\begin{pmatrix}{K(0)} \\\vdots \\{K(i)} \\\vdots \\{K\left( {n - 1} \right)}\end{pmatrix}*\begin{pmatrix}{E(1)} \\\vdots \\{E\left( {i + 1} \right)} \\\vdots \\{E(n)}\end{pmatrix}} = {{{K(0)}*{E(1)}} + \ldots + {{K(i)}*{E\left( {i + 1} \right)}} + \ldots + {{K\left( {n - 1} \right)}*{E(n)}}}}$

In the correlation sums S thus determined, it is possible to search forthe maximum and compare the maximum of the correlation sums S with aprescribed threshold value and, thus, determine whether the prescribedsynchronization sequence K(i) is included in the received signal E(1)and, if so, where it is located in the received signal E(1) and thus tworadio stations are synchronized with one another or data are detected onto which an individual spread code has been modulated in the form of asynchronization sequence K(i).

FIG. 4 shows an efficient hierarchical correlator for synchronizationsequences, Golay sequences X, Y of length nx and ny respectively beingused as constituent sequences K1, K2. The correlator consists of twoseries-connected matched filters (FIG. 4 a) which are respectivelyformed as efficient Golay correlators. FIG. 4 b shows the matched filterfor the sequence X, and FIG. 4 c shows the matched filter for thesequence Y.

The following designations apply in FIG. 4 b:

n = 1, 2, . . .NX ny length of sequence Y nx length of sequence X NXwith nx = 2^(NX) DX_(n) DX_(n) = 2^(PX) ^(n) PX_(n) permutation of thenumbers {0, 1, 2, . . ., NX-1} for the partial signal sequence X WX_(n)weights for the partial signal sequence X from (+1,−1,+i or −i).

The following designations apply in FIG. 4 c:

n = 1, 2, . . .NY ny length of sequence Y NY with ny = 2^(NY) DY_(n)DY_(n) = 2^(PY) ^(n) PY_(n) permutation of the numbers {0, 1, 2, . . .,NY-1} for the partial signal sequence Y WY_(n) weights for the partialsignal sequence Y from (+1,−1,+i or −i).

Moreover, the following definitions and designations are valid in thisvariant design:

-   -   a_(n)(k) and b_(n)(k) are two complex sequences of length 2^(N),    -   δ(k) is the Kronecker delta function,    -   k is an integer representing time,    -   n is the iteration number,    -   D_(n) is the delay,    -   P_(n), n=1, 2, . . . , N, is an arbitrary permutation of the        numbers {0, 1, 2, . . . , N−1},    -   W_(n) can assume the values +1, −1, +i, −i as weights.

The correlation of a Golay sequence of length 2^(N) can be carried outefficiently as follows:

The sequences R_(a) ⁽⁰⁾(k) and R_(b) ⁽⁰⁾(k) are defined as R_(a)⁽⁰⁾(k)=R_(b) ⁽⁰⁾(k)=r(k), r(k) being the received signal or the outputof another correlation stage.

The following step is executed N times, n running from 1 to N:

CalculateR _(a) ^((n))(k)=W* _(n) *R _(b) ^((n−1))(k)+R _(a) ^((n−1))(k−D _(n))AndR _(b) ^((n))(k)=W* _(n) *R _(b) ^((n−1))(k)+R _(a) ^((n−1))(k−D _(n))

In this case, W*_(n) designates the complex conjugate of W_(n). If theweights W are real, W*_(n) is identical to W_(n).

R_(a) ^((n))(k) is then the correlation sum to be calculated.

An efficient Golay correlator for a synchronization sequence of length256 (2⁸) chips in the receiver generally has 2*·8−1=15 complex adders.

With the combination of hierarchical correlation and efficient Golaycorrelator, a hierarchical code—(described by two constituent sequencesX and Y)—of length 256 (2⁴·2⁴) requires only 2·4−1+2·4−1=14 complexadders (even in the case when use is made of four-valued constituentsequences).

This reduces by 7% the outlay on calculation, which is very high for theprimary synchronization in CDMA mobile radio systems, because efficienthierarchical correlators and Golay correlators can be combined. Apossible implementation of the overall correlator, an efficienttruncated Golay correlator for generalized hierarchical Golay sequences,is shown in FIG. 5. This is also designated as a truncated Golaycorrelator, because one of the outputs is truncated in specific stages,and instead of this another output is used as input for the next stage.

The vector D is defined by D=[128, 16, 64, 32, 8, 4, 1, 2] and W=[1, −1,1, 1, 1, 1, 1, 1]. This correlator requires only 13 additions percalculated correlation sum.

By comparison with a sequence having a simple hierarchical orGolay-supported structure, the generalized hierarchical Golay sequenceoffers advantages based on more efficient options for calculating thecorrelation sum with the aid of this Golay sequence. However,simulations exhibit good results with regard to slot synchronizationeven in the case of relatively high frequency errors.

The hierarchical Golay sequences are compared below with the two simplemethods.

FIG. 6 shows firstly an efficient correlator for simple hierarchicalsequences, and a simple correlation method for the hierarchicalcorrelation.

The hierarchical correlation consists of two concatenated, matchedfilter blocks which, in each case, carry out a standardized correlationvia one of the constituent sequences. It is assumed that the correlationvia X₁ (16-symbol accumulation) is carried out before the correlationvia X₂ (16-chip accumulation). This is one implementation option,because the two matched filter blocks (enclosed in dashed lines in FIG.6) are linear systems which can be connected in any desired sequence.240 n delay lines with the minimum word length can be implemented inthis way since no accumulation is performed in advance and, therefore,no signal/interference gain is achieved. Here, n designates theoversampling factor, that is to say how many samples are carried out perchip interval.

As already mentioned, one or both of the matched filter blocks again canbe replaced by a correlator for a (generalized) hierarchical sequence orby an efficient Golay correlator (EGC).

FIG. 7 shows a simple correlation method for the efficient Golaycorrelator (EGC) for a simple Golay sequence. The design of an efficienthierarchical Golay correlator corresponds to an efficient correlator forsimple hierarchical sequences (see FIG. 6), with the exception that twoadders can be omitted.

FIG. 8 now shows an efficient Golay correlator for a generalizedhierarchical Golay sequence. The saving of two adders from 15 addersclearly reduces the complexity of the method accordingly.

FIG. 9 shows simulation results, the slot-synchronization step havingbeen investigated in a single-path Rayleigh fading channel with 3 km/hfor various chip/noise ratios (CNR) without and with frequency errors.It is shown that, by comparison with another synchronization code,designated as S_(new) below, the above-defined synchronization code,designated as GHG below, is just as well suited in practice with regardto the slot-synchronization power. Results are available for the use ofaveraging with 24 slots. A secondary synchronization channel, which isbased on a random selection from 32 symbols, is transmitted in commonwith the primary synchronization channel (PSC). The graph shows thatthere is no substantial difference between the synchronization codeS_(new) and the generalized hierarchical Golay synchronization code GHGfor no frequency error and for a frequency error of 10 kHz.

The proposed synchronization sequence GHG has better autocorrelationproperties than S_(old) (dotted curve), particularly in the case of 10kHz. The graph shows that the synchronization properties of GHG are thusoptimal with reference to the practical use. S_(old) is a hierarchicalcorrelation sequence that is not especially optimized for frequencyerrors.

The use of the generalized hierarchical Golay sequences for the primarysynchronization channel (PSC) thus reduces the computational complexityat the receiving end; the complexity is reduced to only 13 additions bycomparison with the conventional sequences of 30 additions and/or bycomparison with Golay sequences of 15 additions per output sample.

The simulations show that the proposed synchronization sequence GHG havegood synchronization properties in the case both of low and ofrelatively high errors. Because of a lower computational complexity,less specific hardware is required for implementation, and a lower powerconsumption is achieved.

Although the present invention has been described with reference tospecific embodiments, those of skill in the art will recognize thatchanges may be made thereto without departing from the spirit and scopeof the invention as set forth in the hereafter appended claims.

1. A method for synchronizing a base station with a mobile station, themethod comprising the steps of: forming a synchronization sequence y(i)of length n, to be emitted by the base station, in accordance with thefollowing relationship from a first constituent sequence x1 of length n1and a second constituent sequence x2 of length n2: y(i)=x₂(i modn₂)*x₁(i div n₂) for i=0 . . . (n₁*n₂)−1; and forming at least oneconstituent sequence x₁ or x₂ in accordance with the followingrelationship from a third constituent sequence x3 of length n3 and afourth constituent sequence x4 of length n4:x ₁(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1; orx ₂(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1.
 2. A method for synchronizing a base station with a mobilestation as claimed in claim 1, wherein the synchronization sequence y(i)is of length 256, and the constituent sequences x1, x2 are of length 16.3. A method for synchronizing a base station with a mobile station asclaimed in claim 1, wherein at least one of the constituent sequences x1or x2 is a Golay sequence.
 4. A method for synchronizing a base stationwith a mobile station as claimed in claim 3, wherein at least one of thetwo constituent sequences x₁ or x₂ is a Golay sequence which is based onthe following parameters: delay matrix D¹=[8, 4, 1, 2] and weight matrixW¹=[1, −1, 1, 1]; or delay matrix D²=[8, 4, 1, 2] and weight matrixW²=[1, −1, 1, 1].
 5. A method for synchronizing a base station with amobile station as claimed in claim 1, wherein x₃ and x₄ are identicalGolay sequences of length 4 and are based on the following parameters:delay matrix D³=D⁴=[1, 2] and weight matrix W³=W⁴=[1, 1].
 6. A methodfor synchronizing a base station with a mobile station as claimed inclaim 3, wherein a Golay sequence a_(N) is defined by the followingrecursive relationship:a ₀(k)=δ(k) and b ₀(k)=δ(k)a _(n)(k)=a _(n-1)(k)+W _(n) ·b _(n-1)(k−D _(n)),b _(n)(k)=a _(n-1)(k)−W _(n) ·b _(n-1)(k−D _(n)), k=0, 1, 2 . . . ,2^(N), n=1, 2, . . . , N, δ(k) Kronecker delta function.
 7. A method forsynchronizing a base station with a mobile station as claimed in claim1, wherein the synchronization sequence y(i) is received by a mobilestation and processed for synchronization purposes.
 8. A method forsynchronizing a base station with a mobile station as claimed in claim1, wherein in order to determine a prescribed synchronization sequencey(i) contained in a received signal sequence, correlation sums of thesynchronization sequence y(i) are determined in the mobile station withthe aid of corresponding sections of the received signal sequence.
 9. Amethod for synchronizing a base station with a mobile station as claimedin claim 8, at least one efficient Golay correlator is used to determineat least one correlation sum.
 10. A transmitting unit comprising: a partfor storing or forming a synchronization sequence y(i), which can beformed in accordance with the following relationship from a firstconstituent sequence x1 of length n1 and a second constituent sequencex2 of length n2: y(i)=x₂(i mod n₂)*x₁(i div n₂) for i=0 . . . (n₁*n₂)−1,wherein it is further possible to form at least one constituent sequencex₁ or x₂ in accordance with the following relationship from a thirdconstituent sequence x3 of length n3 and a fourth constituent sequencex4 of length n4:x ₁(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1; orx ₂(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1, and a part for emitting the synchronization sequence y(i) forsynchronization with a receiving unit.
 11. A mobile station comprising:a part for receiving a received signal sequence; and a part fordetermining a synchronization sequence y(i), which can be formed inaccordance with the following relationship from a first constituentsequence x1 of length n1 and a second constituent sequence x2 of lengthn2: y(i)=x₂(i mod n₂)*x₁(i div n₂) for i=0 . . . (n₁*n₂)−1, wherein itis further possible to form at least one constituent sequence x₁ or x₂in accordance with the following relationship from a third constituentsequence x3 of length n3 and a fourth constituent sequence x4 of lengthn4:x ₁(i)=x₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1; orx ₂(i)=x ₄(i mod s+s*(i div sn ₃))*x ₃((i div s)mod n ₃), i=0 . . . (n ₃*n ₄)−1.
 12. A mobile station as claimed in claim 11, wherein the partfor determining the synchronization sequence y(i) includes at least oneefficient Golay correlator.
 13. The mobile station as claimed in claim11, wherein the part for determining the synchronization sequence y(i)includes two series-connected matched filters which are designed asefficient Golay correlators.
 14. A method for transmitting and receivingsynchronization sequences, the method comprising the steps of: composinga synchronization sequence from two constituent sequences, wherein saidsynchronization sequence is structured having the followingcharacteristics:y(i)=x ₂(i mod s+s*(i div sn ₁))*x ₁((i div s)mod n ₁), i=0 . . . (n ₁*n ₂)−1, where y(i) is the synchronization sequence having a length of(n₁*n₂) from two constituent sequences x₁ and x₂ of length n₁ and n₂;repeating a first constituent sequence in accordance with the number ofelements of a second constituent sequence; modulating all the elementsof a specific repetition of the first constituent sequence with thecorresponding element of the second constituent sequences; and mutuallyinterleaving the repetitions of the first constituent sequence.
 15. Amethod for transmitting and receiving synchronization sequences asclaimed in claim 14, wherein a constituent sequence x₂ is composed fromtwo constituent sequences x₃ of length n₃ and x₄ of length n₄ inaccordance with the formula x₂(i)=x₄(i mod s+s*(i div sn₃))*x₃((i divs)mod n₃), i=0, . . . (n₃*n₄)−1, or is a Golay sequence.
 16. A methodfor transmitting and receiving synchronization sequences as claimed inclaim 14, wherein a constituent sequence x₂ is composed from twoconstituent sequences x₃ of length n₃ and x₄ of length n₄ in accordancewith the formula x₂(i)=x₄(i mod s+s*(i div sn₃))*x₃((i div s)mod n₃),i=0 . . . (n₃*n₄)−1, or is a Golay sequence.